Pith Number

pith:3OZOEQ4A

pith:2016:3OZOEQ4ACJL3SXALCW5SOBUICW

not attested not anchored not stored refs pending

Spectral atoms of unimodular random trees

Justin Salez

arxiv:1609.09374 v1 · 2016-09-29 · math.PR · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3OZOEQ4ACJL3SXALCW5SOBUICW}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:03:38.037821Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbb2e243801257b95c0b15bb27068815b979324c64f986360314514d865e2392

Aliases

arxiv: 1609.09374 · arxiv_version: 1609.09374v1 · doi: 10.48550/arxiv.1609.09374 · pith_short_12: 3OZOEQ4ACJL3 · pith_short_16: 3OZOEQ4ACJL3SXAL · pith_short_8: 3OZOEQ4A

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3OZOEQ4ACJL3SXALCW5SOBUICW \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: dbb2e243801257b95c0b15bb27068815b979324c64f986360314514d865e2392

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c75b17f1944c76e12d83c0ab3d7f06f5b54b5ba59d77871b0e026c9c0ccfdcbe",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-09-29T15:00:37Z",
    "title_canon_sha256": "264a70367525442a626c88f562fe2fcb5c08df3dc3c3b09a1fc3d4f9fcda0534"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.09374",
    "kind": "arxiv",
    "version": 1
  }
}